Stabilization of underactuated planar acrobot based on motion-state constraints |
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| Institution: | 1. School of Automation, China University of Geosciences, Wuhan, Hubei 430074, China;2. School of Computer Science, Tokyo University of Technology, Hachioji, Tokyo 192-0982, Japan;3. School of Enginering, University of Guelph, Guelph, Ontario, Canada, N1G 2W1;1. A.N. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, 2/10 Dm. Pozharskoho St., 61046 Kharkiv, Ukraine;2. 377 H Administration Building, MC-348, 506 South Wright Street, Urbana, IL 61801, USA;1. Department of Architecture, Chulalongkorn University, Bangkok 10330, Thailand;2. Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia;1. University of Cagliari, DICAAR—Department of Civil and Environmental Engineering and Architecture, via Marengo, 2, I-09123 Cagliari, Italy;2. Intes GmbH, Schulze-Delitzsch-Straße 16, D-70565 Stuttgart, Germany;3. Technische Universität Dresden, Institut Statik und Dynamik der Tragwerke, Schumann-Straße 10, D-01062 Dresden, Germany;4. University of Sassari, DADU—Department of Architecture, Design and Urban Planning, Asilo Sella, via Garibaldi, 35, I-07041 Alghero (SS), Italy |
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| Abstract: | An underactuated planar acrobot (UPA) is a two-link manipulator with a passive first joint. The control objective for a UPA in a horizontal plane is to move it from an initial position and stabilize it at a target position. Since a UPA is not small-time locally controllable, motion control is a big challenge. This paper presents a new control strategy based on constraints on the motion state. First, constraints on the angles and angular velocities of the two links are devised by integrating the dynamic equation of the UPA. Next, the state constraints are analyzed to discover the motion characteristics. Then, the optimal target position is obtained by solving a motion optimization problem that incorporates those characteristics. Finally, a control strategy based on the Lyapunov function method is devised to achieve the control objective. A numerical example demonstrates the validity of the control strategy. |
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| Keywords: | Nonlinear control Underactuated planar arcobot Motion-state constraints Lyapunov control |
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